Existence results for first order discontinuous differential equations of general form

Given a real interval J = [t₀,t₁], consider the implicit initial value problem (IVP) (1.1)f(t,x(t),x′(t)) =0  a.e. on  J,  x(t0)=x0,https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780367812027/499b2676-17a6-4805-9fd8-78c8baf0b813/content/eq350.tif"/>